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Title: Device Independent Playground: Investigating and Opening up a Quantum Black Box
Keywords: nonlocality, quantum, foundations, entanglement, physics
Issue Date: 19-Apr-2014
Citation: YANG TZYH HAUR (2014-04-19). Device Independent Playground: Investigating and Opening up a Quantum Black Box. ScholarBank@NUS Repository.
Abstract: In this thesis, we study the concept on nonlocality in the device independent regime, focusing both on the fundamental as well as its applications. I first review how the dissatisfaction with the concept of quantum entanglement led to the consideration of the local hidden variable model, which however does not recover the predictions of quantum theory and was indeed experimentally refuted. The fact that nature cannot be described with local variables is termed nonlocality. However, it turns out that it is impossible to have arbitrary no-signalling correlations. This shows that there is more to quantum statistics than the no-signaling character, and opens up the possibility of sharpening our fundamental understanding with yet an undiscovered physical principle. I review a few of the proposals in this direction, such as macroscopic locality, information causality and a mathematical tool which can be used to bound the nonlocality of quantum correlations, as a hierarchy of semi definite optimization. In each of these proposals, I present new results which allow us to better understand the role of nonlocality in nature. The second part of the thesis focuses on the usage of nonlocality in the regime of device independent assessment of quantum resources. In particular, this work focuses on "self testing", that is the certification of the states and measurement operators inside a black box, solely based on the observable statistics they produce. It is remarkable that this is possible at all, given the fact that one does not even assume the dimension of the underlying physical system; furthermore, self-testing can at times be based on a single number, e.g. the amount of violation of a particular Bell inequality. Here I report two approaches to robustness. The first one, based on analytical estimates (triangle inequalities and the like), can tolerate only a tiny deviation from the ideal case. The second one exploits semi-definite optimization to improve the robustness by orders of magnitude, making it possible to certify actual experiments. Furthermore, the latter method is very versatile: it can be applied to various self-testing scenarios and can be used to extract a few other important quantities of a black box in an efficient way.
Appears in Collections:Ph.D Theses (Open)

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